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BDDC Deluxe for Isogeometric Analysis

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Domain Decomposition Methods in Science and Engineering XXII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 104))

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Abstract

The main goal of this paper is to design, analyze, and test a BDDC (Balancing Domain Decomposition by Constraints, see [12, 23]) preconditioner for Isogeometric Analysis (IGA), based on a novel type of interface averaging, which we will denote by deluxe scaling, with either full or reduced set of primal constraints. IGA is an innovative numerical methodology, introduced in [17] and first analyzed in [1], where the geometry description of the PDE domain is adopted from a Computer Aided Design (CAD) parametrization usually based on Non-Uniform Rational B-Splines (NURBS) and the same NURBS basis functions are also used as the PDEs discrete basis, following an isoparametric paradigm; see the monograph [10]. Recent works on IGA preconditioners have focused on overlapping Schwarz preconditioners [3, 5, 7, 9], multigrid methods [16], and non-overlapping preconditioners [4, 8, 20].

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133, Milano, Italy

    L. Beirão da Veiga, L. F. Pavarino & S. Scacchi

  2. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, USA

    O. B. Widlund

  3. Extreme Computing Research Center, King Abdullah University of Science and Technology, Thuwal, 23955, Saudi Arabia

    S. Zampini

Authors
  1. L. Beirão da Veiga
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  2. L. F. Pavarino
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  3. S. Scacchi
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  4. O. B. Widlund
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  5. S. Zampini
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Corresponding author

Correspondence to L. F. Pavarino .

Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Technische Universität München, Garching, Germany

    Thomas Dickopf

  2. Section de Mathématiques, Université de Genève, Genève, Switzerland

    Martin J. Gander

  3. Laboratoire Analyse, Geométrie & Applications, Université Paris XIII, Villetaneuse, France

    Laurence Halpern

  4. Institute of Computational Science, University of Lugano, Lugano, Switzerland

    Rolf Krause

  5. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Luca F. Pavarino

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da Veiga, L.B., Pavarino, L.F., Scacchi, S., Widlund, O.B., Zampini, S. (2016). BDDC Deluxe for Isogeometric Analysis. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_2

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